I attack the small neutral ones close by first. Then I select all of my nanos and quick tap bases repeatedly. Unfortunately, it doesn't take much strategy. Just keep reselecting everything and tapping each base you don't own. You can beat each level in about 2 minutes. One of the fastest hard badges I've ever earned.
On the harder levels, it is very important that you keep the zombies from building up in adjacent squares. I kept my soldiers attacking every turn, if for nothing else, just to kill zombies. I also tried to keep my base in close to a perfect square to minimize the number of adjacent squares to my fort.
 "Nano War"){kind=icon}
 "A Duck Has An Adventure"){kind=icon}
 "Paladog"){kind=icon}
 "Ring Pass Not"){kind=icon}
 "Creeper World: Evermore"){kind=icon}
 "Rebuild"){kind=icon}
 "Liquid Measure 2"){kind=icon}